Grandfather Paradox

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Rarity: How in Equestria is my travelling in time supposed to prove that time travel is impossible? Twilight: I explained this Rarity. Travel back along a given time line can't be possible, because it could violate causality — do you know about the Grandmother Paradox? Rarity: No. Twilight: Suppose you travelled back in time to a point before you, and your parents, were born, and you killed your maternal grandmother... Rarity: Why would I ever want to do that? My grandmother is a delightful lady. Even if she does insist on wearing those dreadful frocks with such old fashioned sleeves. Twilight: But hypothetically — suppose you did — by accident — Rarity: I would have trouble — she's a tough old mare. Twilight: Yes, but, theoretically you could do it — when she was young. But then she would never give birth to your mother, so you would never be born — so you could never go back in time to kill her — it's a paradox — see!

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The grandfather paradox is a type of Temporal Paradox. The name comes from the most famous variation, namely "what would happen if you traveled back in time and killed your own grandfather?" However, it also applies to anything that happens while time traveling that should logically make your original time travel trip impossible or unnecessary.

So, then, killing your grandfather causes you to not exist, and since you don't exist, you never killed him. Which means he survives, so you exist, so you do go back to kill him. Which means he doesn't, so you don't; therefore he does, so you do, etc. Are you confused yet?

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Alternately, this whole snafu can be ignored outright if you're using Alternate Universe-style time travel, where the time period you came from is separate from (and unaffected by) any meddling you do in the past. The downside to this is that returning "home" might be a tricky matter....

Examples:

The original Eclipse Project would have caused one of these. The goal of the project was to use the gate to go back 400 years into the past and kill Zeref before he became the Black Wizard. Chapter 436, which is an entire chapter on Zeref's past, reveals that Zeref was the one who created the Eclipse Gate. Killing him would cause the gate to never exist — which would render the need for the Eclipse Project nil, allowing Zeref to survive, and so on and so forth. Time would be stuck in an endless loop. This is (presumably) also the same reason why Zeref never used the gate for its original purpose: to save his little brother Natsu from his premature death. Had he done so, he would have had no reason to create the gate, which would causes Natsu to die again, etc. Notably, the only known instances where the gate was used and didn't backfire and cause some temporal problems is when characters used it to send others to the future and not the past.

The Alvarez Empire arc reveals that Zeref's goal is to use Neo Eclipse to subvert the paradox problem. Rather than being stuck in an endless loop, Zeref intends to create an entirely new timeline to take the place of the current one. His chosen point is the time before he became immortal, so that way he can prevent all the tragedies that befell him and his brother. While that would ensure that the events of the manga would never happen, there is no guarantee that any of the characters in the current timeline would be born and/or suffer even more tragedy — for all anyone knows, Zeref could just be hastening the apocalypse. Unfortunately, Zeref has gone so far beyond the Despair Event Horizon that he simply doesn't care about any of that, as he has already come to reject the current world in favor of his new one.

Steins;Gate explains that this is why Okabe been failing to change the timeline in his favor, specifically when he needs to save Kurisu from being stabbed. The whole plot kicked off when Okabe accidentally sent the first D-Mail after seeing Kurisu lying in a pool of blood, drastically changing events so that, among other things, the above event was prevented from happening, allowing Okabe and Kurisu to fall in love with each other. Without that, he wouldn't even be trying to save Kurisu in the first place. However, nothing says that he can't change events so that they're similar enough that his past self effectively does the same thing as before.

Comic Books

IDW's Back to the Future establishes 1985-A (the hellish 1985 from Back to the Future Part II) as an impending grandfather paradox, as Doc Brown finds out that his alternate universe double has been lobotomized. If Doc Brown never builds the time machine, then Old Biff can't give the almanac to his 1955 self; and if he doesn't give the almanac to himself, then 1985-A can't happen...

Miguel O'Hara from Spider-Man 2099 (2014 series) isn't sure exactly what would happen to him if his grandfather Tiberius Stone dies on his watch and he's not eager to find out. This leaves Miguel in the unenviable position of protecting a man he quite rightfully despises.

Defied in the 2010 Dynamite run of Vampirella when Conqueror from the Future Professor Quatermass visits his great-grandfather to ensure that he'll invent time travel ahead of schedule to further his plans. When his great-grandfather hesitates, Quatermass shoots him only after asking him if his grandfather is safe at home.

During the time travel arc of Thunderbolts, the current team ends up in New York, back in the days when the first team of Thunderbolts was still active and still serving as Zemo's disguised Masters of Evil. Due to a long chain of events, the past version of Fixer finds out about his future by secretly hacking the present Fixer's files, and the two get into an argument that causes the present Fixer to kill his past self by engaging a self-destruct built into his past-self's armor. This causes reality to start imploding in on itself, and the destruction of everything is only averted when Fixer has Centurius erase his memories and de-age him so that he can take his past self's place, creating a Stable Time Loop. This is ultimate fixed in a later Thunderbolts story when Kobik, the living Cosmic Cube in the form of a little girl, undoes the loop by erasing past-Fixer's death.

The Morphin' Grid prevents this in Mighty Morphin' Power Rangers: Shattered Grid as it decides to split apart every single era of the Power Rangers timeline into its own little universe after Lord Drakkon murders Tommy Oliver during his early Green Ranger days.

Fan Works

My Family and Other Equestrians: Blade Star has been sent back in time to near the events of the season 2 finale of My Little Pony: Friendship Is Magic, thanks to a Weeping Angel. How does he decide to get back? By causing a Grandfather Paradox. If he were to do something at that moment in the past, it would have a ripple effect on his own future, causing everything to change since Blade Star's arrival in Equestria. This would mean that the timeline in which Apple Bloom and Blade Star went to Time Turner's shop and encountered the Weeping Angel would not happen, or at least, happen differently. He would change the past, but therefore have never existed to come back and change the past in the first place. He then concludes that the Weeping Angel itself would become a paradox, as it fed off of something that had no time energy because it didn't exist. In Layman's Terms, he would potentially be brought back to his point of origin, and the angel would be caught in the paradox.

Blade Star then decides to confront Queen Chrysalis and expose her to the ponies earlier than in canon, severely injuring her in the process. The paradox this causes is so huge that Discord has to come in and fix the mess, stating that this was simply way too much chaos for one being, even by his standards.

Films — Live-Action

The plot of the first Back to the Future may be the most well-known example, even though it's a) not Marty's grandfather it involves and b) he doesn't kill him, but rather accidentally takes his place as his mother's object of affection. The rest of the movie has Marty trying to correct things before he's erased from existence.

Played with in Enter Nowhere, in which a young woman about to rob a convenience store finds herself transported to an isolated cabin where two strangers are similarly stranded, and where a mysterious rifleman is creeping around in the woods. The rifleman is her grandfather, who'd died in WWII without ever seeing his baby daughter, and the others are the still-pregnant mother she never knew and the son she won't live to see grow up. Inverted in that the grandfather actually kills her and causes her son to disappear in the process, leaving it up to her mom-to-be to save her own dad and thus, all four lives. Played straight in that it's implied the three were sent back in time to avert the grandfather's death because the convenience-store clerk has supernatural power and wanted to give them all another chance ... one meaning that, since her Mom survived to stop her from becoming a criminal, the robber wouldn't have confronted the clerk in the first place.

Inverted in Stargate Continuum, where Cam Mitchell winds up going back in time, and eventually (ten years down the road) keeping his Grandfather alive as a way of setting right what Ba'al had messed up. Said paradox was directly referenced before, when Mitchell found out that he doesn't exist in the new timeline because Ba'al killed his grandfather.

Discussed and ultimately averted in Terminator Genisys. Sarah Connor tells the T-3000 (her son John Connor) that he can't kill either her or Kyle Reese because they're his parents and that would negate his existence. John retorts that since all three of them are outside their natural timelines, there truly is "no fate" and he can thus kill them without erasing himself.

The 2002 film version of The Time Machine (2002) is inconsistent in how it deals with this. The first act demonstrates that it is actually impossible to create a paradox; Alexander builds his time machine so he can save his love Emma from dying, but no matter what he does, she always ends up dying in one way or another, because if she didn't, he wouldn't build the machine and save her. However, the third act throws this out the window when Alexander travels from 802,701 to even further in the future, discovers that the Morlocks have conquered the Earth, and then goes back to 802,701 to destroy them so that they can't. By the first act's logic, it should be impossible for him to do this, since he's erasing the reason for his own actions, but it works perfectly anyway.

The happy ending for Special Constable Tom Campbell in the Doctor Who spin-off film Daleks' Invasion Earth: 2150 A.D. has him returning in Tardis to a point a few minutes before his departure from 1960s Earth, and arresting the burglars who attacked him and caused him to stumble concussed into Tardis in the first place. There is no acknowledgement of the major paradox problems this would cause, such as there being two different Toms wandering around.

In Eric, the wizard Rincewind is time-traveling and says that since he's gone back to the beginning of time due to someone using him as a genie wishing to live forever (i.e. beginning to end of time), and he says that he would have to wait around for a while until he could kill his grandfather which is "the only aspect of time travel that really appealed to him".

In Time Enough for Love, Lazarus Long just glosses over the possibility of creating a paradox while time-traveling by saying that it's impossible to create one. So he has sex with his mother, meets his younger self, enlists in the Army and fights in World War I. It Makes Sense in Context.

In The Door into Summer, this is boiled down to the time-traveler protagonist waiting just outside of a room where he also is prior to his time-traveling activities, and briefly wondering what would happen if he ran in and slashed his counterpart's throat. He doesn't do it, of course, because that would be stupid and accomplish nothing, but he notes in present tense that he still hasn't figured it out.

The Charles Stross novella Palimpsest has a twist: killing your own grandfather is the initiation rite for the Time Police. The graduation ceremony is stepping back in time a few minutes and killing yourself.

Paradoxically inverted in "Grandpa", a short story by Edward M. Lerner. In it the protagonist, Professor Fitch, survives two assassination attempts by his grandson, and preempts a third by deciding not to have children.

In Johnny and the Bomb, Bigmac suggests going back in time to kill Hitler. Johnny warns him of the dangers should he accidentally kill his grandfather, but Bigmac says it's safe since his grandfather doesn't look anything like Hitler. (Fortunately, by the time they obtain actual time travel, he's forgotten the plan.) Then they fall victim to an actual grandfather paradox: their time travel results in Wobbler's grandfather being killed in a World War II bombing.

In Michael Crichton's Timeline, one of the protagonists raises this paradox to the Corrupt Corporate Executive who's trying to send them back in time. The latter changes the subject to a long discussion about how it would be nearly impossible for one person to make the Mets beat the Yankees (ie, the forces of history are too large for one person to decisively change). When the protagonist presses the point, the Exec Hand Waves it and moves on.

The end of The Saga of Darren Shan explains how the story is an endless paradox because the rule of Destiny is that if you kill someone, somebody else will take their place and do exactly as they would do (as an example, Evanna says that if you were to kill Hitler, somebody else would've taken his place and done exactly as he did.) and seeing as Darren goes through everything just to go back in time to stop the whole thing from happening, someone else will see the Cirque, join Mr.Crepsley and go on all the exact adventures Darren did, eventually having to stop themselves from seeing their best friend talking to Mr.Crepsley and then someone ELSE taking THEIR place and so on. Darren says that afterward you could read the books again and change all the names and it'd still be technically correct.

Inverted in two separate ways in Rant: Traveling back in time to kill your parents will cause you to be outside of time, and therefore immortal (in-universe this is known as "severing ties"). Going back and impregnating your mother, or a direct matriarch of your family (grandmother, great-grandmother) will result in gaining heightened faculties (this is known in-universe as "stoking". Combo points for impregnating each one down the line until you are born.)

Gregory Benford's Timescape describes a unique, quantum-mechanical approach to Grandfather Paradoxes. If a time-travelling signal were to prevent its own transmission, the signal and everything involved in triggering it would be in an indeterminate state where it neither does, nor doesn't, occur — like Schrödinger's Cat before the box is opened.

In one classic sci-fi story, the protagonist decides to try to commit suicide in a grand way by going back in time to shoot his grandfather. He does so. Nothing happens, so he turns the gun on himself. The narrative continues on to note that the sound of the gunshot does nothing to disturb his grandmother and his grandfather's best friend as she tells him to make sure he pulls out in time...

Discussed in Stephen King's 11/22/63. Though he initially hand-waves, King does answer the question implicitly: nothing would happen to the traveler. People who go through the portal are "out" of the timestream and thus not eliminated as a result of their actions. Although progressively worse things happen to the traveler the more the traveler tries to make a major change to the timeline, and although the traveler will return to the exact moment of departure, the effects of time spent in the past — such as aging — are not reversed.

"Yeah, but what if you went back and killed your own grandfather?" He stared at me, baffled. "Why the fuck would you do that?" That was a good question, so I just told him to go on.

Discussed and inverted in Locksmith's Closet. When Lock and Gary travel into the future and find it uninhabited, Gary remarks that "at least we don't have to worry about our grandkids coming along and shooting us just to see what'll happen."

Happens literally in René Barjavel's novel Le Voyageur imprudent (translated as Future Times Three) written in 1943 (hence the first novel to enunciate the grandfather paradox) where the time-traveler (Pierre Saint-Menoux) tries to assassinate Napoleon Bonaparte before his rise to power: at the last moment, a soldier jumps to take the bullet and save Bonaparte. This soldier is of course the time-traveler ancestor. The time-traveler is then wiped out from existence. There is even an appendix explaining the paradox at length (including the fact that, for the time-traveller, there is no real ending - he is constantly oscillating between existing and non-existing. The ending of the novel however makes it clear he does not exist any more - his fiancée is celibate, and the man he helped build the time machine in the first place is fruitlessly trying to make it work)

In Poul Anderson's Time Patrol stories, you can have effects without causes, so that killing your grandfather merely means you exist without a parent. Fortunately this means you can yank history back on course. Or unfortunately, since in the process you eliminate the future created by the change, and everyone in it.

Discussed in The Dresden Files novel Cold Days, when Harry asks Vadderung what would happen if he were to travel back in time and attempt to kill his grandfather. The answer is that Harry's grandfather would beat him senseless, because Harry's grandfather is Ebenezer McCoy, Harry's mentor and the White Council's Blackstaff. Eventually he gives a more serious answer, it would destroy the current timeline and create two new ones, one where he failed and one where he succeeded.

Parodied in one of Brian Aldiss's "Three Enigma" stories. A time traveler goes back in time and falls in love with his grandmother, causing his grandfather to commit suicide. "I can see this is going to be awkward," says the time traveler as he fades out of existence.

A different take, not involving relatives, is in A Dry, Quiet War by Tony Daniel. The protagonist returns to his home planet after fighting a war twelve billion years in the future at the end of time, apparently to hold back the spread of entropy so the universe has a chance to exist in the first place. He has a run-in with several deserters from that war who are terrorizing the place. If he does anything to harm them however, it changes the future and everything he's fought for has been for nothing.

Doctor Who Expanded Universe: For the Time Lords, Grandfather Paradox is an actual person who went back and, yes, killed his grandfather, which doomed him to a sort of undead temporal limbo. He's the Time Lord equivalent of the Bogeyman, and the splinter group/terrorist cult Faction Paradox considers him their spiritual leader, partly cause it pisses off the Time Lords. We actually meet him. He's quite literally the Anthropomorphic Personification of Future Me Scares Me — he's everybody's evil future self. And Faction Paradox has the entire trope as a sport for initiates. Want to get in? Kill momma. Before you were conceived. At one point, his appearance is described as eerily similar to the Ninth Doctor, which at that point would have been the Doctor's future self. In fact, the first time the Doctor encounters a Faction Paradox agent, the agent calls him "Gramps".

Discussed in Octavia Butler's novel Kindred when Dana finds herself pulled back in time to the antebellum South whenever her ancestor Rufus is in mortal danger. As he comes to treat her more and more like one of the plantation slaves, only the threat of a paradox keeps her protecting his life. Once Rufus has a child, that protection expires.

Happens quite often in Stephen Baxter's Xeelee Sequence books, where entire wars are fought atemporally, causing battles to happen multiple times in different timelines with different outcomes, and where going back in time to give your own side intelligence about your enemy's future actions is a common tactic. Defied in one instance where a character receives information from a timeline that should no longer exist, but the information still remains. The explanation given was that time is flexible, and just because the one particular event that led to him getting that information now had never happened, in some other timeline he had gotten it a different way, and so he ended up still having it.

"Wikihistory" is about a group of Time Travelers, and one of their rules is "no killing Hitler", because it would prevent the invention of time travel itself. There are no such restrictions on other genocidal tyrants, but one must consider the possibility that one is descended from such an individual before eliminating them.

Live-Action TV

The 12 Monkeys episode "Lullaby" has Cassie create a paradox by going back in time and killing Jones immediately after the death of her daughter, before she could start trying to invent time travel. The result is a "Groundhog Day" Loop until Cassie (and Cole, who comes back to help) can figure out what needs to happen to preserve the timeline.

Referenced in Continuum, when terrorists Liber8 attempt to eliminate their adversary Kiera Cameron- both displaced to 2012 from 2077- by killing her grandmother before she can give birth; Kiera attempts to counter this by threatening the pregnant mother of Liber8's founder. The paradox is apparently proven irrelevant when the grandmother of Liber8 renegade Matthew Kellog is killed before she has children and nothing happens to him, but Kiera's ally Alec Sadler notes that lack of evidence is not proof that nothing will happen.

Martha: What if I kill my grandfather? The Doctor: Are you planning to? Martha: No. The Doctor: Well, then.

"Last of the Time Lords": The Master constructs a Paradox Machine specifically to evade the consequences of this paradox, as his army of homicidal laser balls happen to be the descendants of humans, from the end of the universe.

"Demons of the Punjab": When Yaz goes back in time to meet her grandmother Umbreen as a young woman, the Doctor warns her several times about potentially causing one. Saving Prem, Umbreen's first husband, from dying would cause such a paradox, so they have to walk away as he is killed.

The Flash (2014): Avoiding the complications of the Grandfather Paradox is first implied, then confirmed to be the reason that the Reverse Flash aka Eobard Thawne aka Harrison Wells spares Eddie Thawne's life in the "The Man in the Yellow Suit". In the first season finale, Eddie takes advantage of this and shoots himself to erase Eobard from existence. Unfortunately, the ensuing paradox might be why a planet-threatening singularity shows up afterwards. In a later episode, the Reverse Flash returns, being an earlier version of the villain from before he traveled back in time to kill the Flash as a child (it's speculated that he was protected from the paradox by the Speed Force, as he would need to travel back in time again to set all the events into motion).

Later Barry threatens to do this to himself to destroy Savitar, who turns out to be a time remnant of himself (kind of a speed clone) he'll create in the future. If he dies then, he can't create Savitar later on. Savitar says it might, but also points out the above example that Eddie killing himself didn't stop Thawne from eventually coming back and that the rules of time travel don't always completely apply to speedsters so Barry might just be killing himself but leaving Savitar free without anyone to stop him.

Inverted in Haven, where after traveling back in time Duke accidentally saves his grandfather (who had already had a son). When Duke learns who he is, the issue becomes whether he needs to make sure he dies or let him continue living. Turns out it's neither. Duke is a part of a Stable Time Loop in which Sarah Vernon ends up killing Roy Crocker, because he found out from Duke that she was going to kill him, so he went after her first.

Zari: Ball Kick Paradox. You can't kick your own dad in the junk, because you'd erase yourself from the timeline, and there'd be no one to kick your dad in the junk.

Subverted on Timeless when the pilot episode ends with historian Lucy returning from altering the fate of the Hindenburg (it crashed a day later with only two people killed) to find that her sister, Amy, no longer exists. A computer search reveals that Lucy's father, Henry, married the granddaughter of someone who was supposed to die on the Hindenburg and never met Lucy's mother, Carol. Lucy is at first confused how she can exist if her parents never met...then realizes it means Henry was never her father in either timeline.

Averted in Time Trax, which the protagonist claims to be taking place in a time-shifted parallel world instead of their own past (except for the times when the shows writers forget that and treat it as an actual past). A criminal from his own time is attempting to track down an eliminate the ancestors of Darien's old partner, who was involved in a car accident that killed the criminal's girlfriend. The criminal assumes that, by making sure the guy is never born, the accident will never have happened, and she will still be alive. Darien tries to convince him that this isn't how time travel works.

Parodied in The X-Files in "Clyde Bruckman's Final Repose": the title character cites this as a reason why he shouldn't help Mulder and Scully catch a serial killer — because one of the people he might save could be the grandmother of the person who'd invent a time machine that would mean Clyde's father never met his mother and therefore he'd never have been born. As his ability to see the future had made his life a misery, Clyde suddenly realizes that wouldn't be a bad thing after all.

Tabletop Games

Genius: The Transgression's stance on the subject: "And yes, if you kill your own grandmother before your father is born, you will cease to exist. The universe, it turns out, doesn't care that much if your grandmother gets shot in the head and there's no shooter. You still go poof."

The old Doctor Who RPG encourages GMs to be cruel to players who try this. One popular result is that, if you go back in time and point a gun at your grandfather, then the young version of your grandfather will leap out of the way, pull his own gun and shoot you dead. Paradox? What paradox?

The Warhammer 40,000 supplementary material has an Ork warboss who traveled back in time a day and proceeded to kill his past self so he could have two copies of his favorite gun. Unfortunately, this so confused the Orks under his command that the WAAAGH! he was leading fell apart.

Feng Shui goes with a belt-and-suspenders approach. Actually changing history is hard and requires taking possession of feng shui sites; doing something minor like shooting your own grandfather changes nothing. Johnny Wong will return to the present to discover that his grandmother met someone functionally identical to his old grandfather and the only difference is that his name is now Johnny Fong. If you do make the effort to make your changes stick, you can shift history so that you never existed... but accessing the Netherworld (the method of time travel) immediately locks in your personal timeline at that point, and you will never be affected by future shifts. So Johnny Wong returns to a present where he doesn't exist and never did, but he still exists because he's locked to a timeline where he existed. (The Netherworld is full of people who had one too many shifts happen to them and retreated from a world that they no longer know and that no longer knows them.)

Timemaster: One of the corollaries to the game's Laws of Time Travel flat-out states that this is impossible. No matter what you try, you will never be able to kill one of your ancestors. Your enemies, on the other hand, can blow away as many of your ancestors as they feel like, which would erase you from the time stream. Time Corps agents are advised to never talk about their families.

Joining the highest ranks of the Cult of the Doomsday Clock requires that a mage reach through time and kill their past self, making their existence a Paradox and allegedly freeing themselves from the shackles of time. Subverted in that this actually allows an abyssal monster to devour the mage's existence and take their place in the world, since those entities are Paradox incarnate.

Lampshaded in Magic: The Gathering. In the Tarkir block, Sarkhan Vol travels back into the past of his own plane and alters the timeline so that the dragons never went extinct. One of many knock-on effects from this is that Sarkhan himself was never born in the new timeline. However, perhaps due to being a Planeswalker, he still exists as a self-described "orphan of time". For all intents and purposes, he simply popped into existence fully-formed when he returned to the present.

Video Games

Within the semi-canon/non-canon of Telltale's Back to the Future: The Game, Marty does encounter his paternal grandfather and affects his own existence in time.

In Metal Gear Solid 3: Snake Eater, if you kill Major Ocelot instead of just knocking him out, you get the "TIME PARADOX" Nonstandard Game Over. Ocelot is integral to the plot of the previous games in the series, which take place chronologically after Metal Gear Solid 3. Hilariously, the HD re-releases of the game have an achievement/trophy for doing this entitled, "Problem Solved, Series Over."

In one of the demo videos for the RTS game, Achron, they build a mech, then send it back in time to destroy the factory that built it. The way the game handles this is pretty interesting since it involves "time waves" and a point in the past where time manipulation is impossible. Time waves sweep through the timeline from past to future and, to quote the wiki, "a time wave is what makes the past affect the future". So, when a time wave hits the time the factory was destroyed, the factory simply gets destroyed and the mech survives. When the next time wave hits, the mech will be destroyed because the factory doesn't exist in the future and the factory survives and so on. The "final" version of the event is the one when the event hits the point where time is immutable. You know what, just watch the video.

In Chrono Trigger, Marle disappears from existence due to her being mistaken for her ancestor, Queen Leene, who was kidnapped at the time she landed in the past. Since everybody stopped looking for Leene because they thought they had found her, she was killed, thus causing Marle to not exist. Fortunately, Leene hasn't been killed yet, so our heroes are able to go rescue her, which allows Marle to exist again. While this is clearly a grandmother paradox, everyone seems to remember that she existed, at least long enough for her to cause herself to have never existed.

In Pokémon Mystery Dungeon: Explorers of Time/Darkness/Sky, the player character traveled back in time from a Bad Future to change the past. When they succeed, they have just enough time to say one last goodbye to their partner before they fade away. Ultimately averted, as the lack of Ret-Gone makes the point moot.

One of the death scenes in Time Gal has Reika fire her gun into a bunch of cavemen  and promptly dematerialize because she just shot one of her ancestors.

In the true ending of The King of Fighters XIII, Ash stops his time traveller ancestor Saiki from returning to the past after losing the fight to the player. Soon after, Ash fades away taking Saiki with him.

In Space Quest 5, anything that causes Beatrice's death will cause Roger to cease to exist. She is the eventual mother of his son, who saved Roger's life in the previous game. No Bea means no son, no son means Roger was never saved. The death screen will explain this each time.

Invoked in BioShock Infiniteending: Elizabeth travels back in time and kills Booker, her own father, before her conception in every possible timeline, thus forcing the universe to block off all branching timelines where Booker becomes Comstock, kidnaps Booker-from-another-universe's daughter Anna, who grows up to become Elizabeth and develops reality-warping and time-traveling powers as a result of her dimension shift. That way, the only timelines that are left are the ones where Anna/Elizabeth grows up peacefully with a never-baptized Booker.

In the R-Type games, a fanmade theory inspired by the obscure points of the plot, features the main antagonists the Bydo Empire (a race of biomechanical creatures that can directly control technology), created by humans as a weapon in the future. The theory, really shortened, would result in the Bydos understanding how bad and evil their situation was for them. After failing mass suicide different times (because the humans like the player, fighting them, actually made them more powerful), the Bydo would go back in time and destroy humanity when the empire still wasn't created, effectively resulting in a long-term Grandfather's Paradox.

In The Journeyman Project series, it's fairly easy to change something in the past, but, since the Delayed Ripple Effect travels only forward in time, it will not affect the time traveler himself, provided he doesn't return before the wave reaches his point of departure. This is also how, in the first game, the Temporal Security Annex keeps a copy of the world history from being overwritten by a time wave. A disk with the copy is kept in the distant past. If a ripple is detected (somehow), a time agent it sent back to that period to retrieve the copy, which can be then compared in the present to the history in the Annex's data banks to figure out the point of divergence. This is Hand Waved in later games, and the TSA simply knows where and when the change took place without the copy, but an agent still needs to be sent back before the wave hits to avoid him or her becoming part of the new timeline.

Web Animation

A Newgrounds cartoon "Grandbunny Paradox" made fun of this. It featured a bunny and a stick figure. The bunny went back in time to kill his grandmother and finds himself turned into a sheep, because his grandfather married a sheep instead of a bunny. The stick figure decides to do the same and kills his grandmother only to find himself turned into a tomato. He doesn't like being a tomato so he goes back and shoots the guy who sold him the gun to kill his grandmother... only to find himself now holding grenades.

Adam and Jamie decide to put this trope and the My Own Grandpa trope to the test when they went back in time in Irregular Webcomic!. They botch it up when they accidentally swap grandmothers, making each other their grandfathers (Adam is Jamie's grandfather, Jamie is Adam's). This does make them their own great-great-grandfathers, proving that this trope and the My Own Grandpa trope is possible. Myth confirmed! Incidentally, the people that should have been Adam and Jamie's grandfathers themselves went back in time to the Jurassic period, where they were eaten by an Allosaurus that used the time machine to go to the future and become president.

This is just one of the many problems with trying to exploit Time Travel in Homestuck. The past, present, and future of all of the characters are so intertwined with each other that trying to retcon any of them away would lead to a paradox if it were even possible in the first place. The only way to safely use time travel is to ensure you always complete stable time loops, or ensuring that what has to happen will happen/has happened/continues to happen... Tense is also a problem exploited, by the way...

When Schlock Mercenary, ventured into a Time Travel arc, they showed how it might look from the "Grandfather" side of things, only to prove that for the Schlock Universe, there ISN'T a Stable Time Loop in effect. Which is just what they need to save the Galaxy.... In this particulate case, the 'grandchild' is a VDA probe from the future, and the 'grandfather' is the younger version of the probe.

6teen: Jude Lizowski misinterprets this in "Bicker Me Not," where after Jonesy accidentally breaks up George and Gracie Bickerson (an elderly couple that's been married for fifty years), Jude reveals that his own grandparents got married fifty years previously (he never clarifies if they were his mom's parents or his dad's parents). However, Jude never met them, "on account of the fact that they were political rebels who went into hiding" before he was born—after the rest of the gang points out that (assuming Jude's grandparents are still alive) they're probably around the same age as the Bickersons, Jude begins to think that George and Gracie are actually his grandparents. This is what leads to Jude misinterpreting the titular paradox: if George and Gracie break up (in the current timeline) and don't get back together, he'll eventually cease to exist.

In Adventures of Sonic the Hedgehog, one episode in the four episode arc about the Chaos Emeralds starts with Sonic foiling a plot by Dr. Robotnik to prevent his ancestors from marrying and thus eliminate Sonic from the timeline. Sonic succeeds in sending Robotnik packing, but then causes the paradox himself by ordering a chili dog from his maternal ancestor, causing his paternal ancestor to become impatient waiting to be served and leaves. After Sonic disappears, Tails solves the paradox in about a minute by forcing the meeting to happen.

Discussed in an episode of Darkwing Duck where Gosalyn uses Quackerjack's time machine to bring three of DW's ancestors to the present. Darkwing starts to consider the potential consequences, leading to an Explain, Explain... Oh, Crap! realization.

In an episode of Futurama, Fry goes back to Roswell in 1947 and accidentally gets his grandfather killed in an atomic blast while trying to avert this. He doesn't stop existing because he also ends up doing his grandmother, becoming his own grandfather. Or, as he puts it, "I did do the nasty in the pasty." This becomes a key plot point in later episodes, as the extreme inbreeding causes him to have a birth defect that makes him immune to a number of things. This also means that, instead of merely being Professor Farnsworth's lateral ancestor (who is descended from Fry's brother), he is also the Professor's direct ancestor.

GIR: Wait, if you destroyed Dib in the past, then he won't ever be your enemy, (short circuits) then you won't have to send a robot back to destroy him...and then he WILL be your enemy, so you WILL have to send a robot back—(head explodes)

In the final episode of Samurai Jack, Jack finally manages to travel back to his own time and kill Aku. Unfortunately, since his love interest, Ashi, was Aku's daughter, she ends up ceasing to exist. Cruelly, she seems perfectly fine until their wedding day, when she suddenly collapses, realizes Aku would have never fathered her, then vanishes in Jack's arms.

Since it was with Ashi's powers that they returned to the past, if she was never born then how did Jack get back to kill Aku in the first place?

Wonder Warthog employs this with one case of glaring inconsistency. He is hanging out in a bar with Stoneage Warthog and The Hog from the Future (I may have the names wrong), and the latter decides to explore the nature of a paradox by shooting the former with a zapgun. Since Stone-age Warthog was the direct ancestor of the others, they cease to exist, while the city is retroactively turned into a crime-ridden cesspool because WW wasn't around to do anything. The Hogs are then immediately returned (since Future Hog couldn't have killed Stoneage Hog if he didn't exist) and everything is fine...except the city is still a hellhole, necessitating the heroes to fix it the traditional way.

Real Life

While this paradox is almost always associated with time travel, it is actually also a consequence of faster than light travel or communications. The problem is that when a signal travels faster than light, it is possible for the signal to travel faster than the action that caused the signal to be sent. An example would be telling someone to not fire a bullet that you see would hit you. How could you tell them to not fire the bullet if your telling them would prevent you from seeing it and thus telling them?

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